Question

A teacher sits on a rotating stool to demonstrate the conservation of angular

momentum. With her arms outstretched, she rotates at 2.25 rev/s. When the

teacher’s arms are tucked in close to her chest, she rotates at 4.50 rev/s. what

is the ratio of her moment of inertia with outstretched arms to the moment of

inertia with arms tucked in close to her chest?

Answer 1

angular momentum:

$L=\omega I$

where $\omega$ is angular velocity, I is moment of inertia

$\omega =2\pi n$,

where n is revolutions per second

conservation of angular momentum:

$\omega_1 I_1=\omega_2 I_2$

the ratio of her moment of inertia with outstretched arms to the moment of

inertia with arms tucked in close to her chest:

$\frac{I_1}{I_2}=\frac{\omega_2}{\omega_1}=\frac{n_2}{n_1}=2.25/4.5=1/2$